Flow-induced in-line oscillation of two tandem rectangular cylinders has been experimentally studied by free-oscillation tests in a wind tunnel. Only one cylinder of two cylinders was elastically supported easily to move in the in-line direction for reduced mass-damping parameter Cn ≈ 1.5 ; the other was fixed to the tunnel sidewalls. The gap between two tandem cylinders was changed from s=0.3 to 3. We measured the response amplitudes of the oscillatory cylinder in the in-line direction and the vortex-shedding frequency in the wake. The flow around the tandem cylinders was visualized by the smoke-wire method. As a result of the upstream cylinder, an excitation appeared in a wide region of reduced velocity, Vr = 2.5 to 5 at gap ratios of s=0.3 to 2. This excitation was mainly induced by symmetric vortex shedding, the other excitation of Vr =4.5 to 6.5 at wide gap ratios of s=0.75 to 1.5, was induced by alternate Karman vortex shedding, accompanied with unstable limitcycle. The downstream cylinder had an excitation region in a wide range of Vr=3 to 5.5 for the narrow gap distance of s = 0.3 to 0.75, which also seems to be induced by alternate Karman vortex shedding. Furthermore, the downstream cylinder oscillated as a buffeting phenomenon influenced by wake-fluctuation of the upstream cylinder, when gap distance was greater than s = 1.